A Behavioral Foundation of Reward-Risk Portfolio Selection and the Asset Allocation Puzzle

In this paper we suggest a behavioral foundation for the reward-risk approach to portfolio selection based on prospect theory. We identify sufficient conditions for two-fund separation in reward-risk models in general, and for the behavioral reward-risk model in particular. It is shown that a prospect theory investor with piecewise-power function satisfies two-fund separation if the reference point is the risk-free rate, while two-fund separation fails if the reference point is higher than the risk-free rate. We derive a multiple-account version of the behavioral reward-risk model and we perform an empirical analysis on U.S. data to show that this model explains the asset allocation puzzle